The big advantage to using continuous compounding to express growth rates is it avoids the problem of asymmetry in growth rates:
For example, if we use the normal definition and $100 grows to $105 in one time period, that's a growth rate of $105/$100 - 1 = 5% But if $105 decreases to $100, that's a growth rate of $100/$105 - 1 = -4.76%
The problem of asymmetry is those two growth rates, 5% and -4.75% are not equal up to a sign.
But if you use continuous compounding the growth rate in the first case is ln(105/100) = 0.04879.
And the growth rate in the second is ln (100/105) = -0.04879.
Those two growth rates are definitely the negative of each other.
